We will explore these questions explicitly in the context of the SYK model [1]}, [2]}, [3]}, and in a related model where the Majoranas are replaced by Pauli matrices (see for example [4]}). The SYK model is a quantum mechanical system with \(N\)  Majorana fermions, with an all-to-all interaction of \(p\)  fermions at a time, where the strength of each such \(p\) -interaction is an independent random Gaussian. In the Pauli matrices model there are \(N\)  spin \(1/2\)  Hilbert spaces with a general random \(k\) -local interaction made out of Pauli matrices. In the large \(N\)  limit, the SYK model has a nearly-conformal symmetry in the IR, and fluctuations around it are described by a Schwarzian effective action, which is the same dynamics that describes JT gravity on \(\text{NAdS}_2\)  [5]}, [6]}. This provides a useful context for studying holographic relations where we can do some calculations directly in the quantum mechanical system. One of our main aims is to study semiclassical generalizations of the TFD from the boundary perspective, in contrast with earlier works which have focused primarily on calculation in the bulk holographic picture. We will mainly do calculations in a double scaled limit of SYK [4]}, [8]}, where we take \(p\)  and \(N\)  to infinity with \(p^2/N\)  fixed, using the chord diagram approach to calculations in this limit discussed in [9]}, [10]}, but the main conclusions carry over to the usual SYK large \(N\)  limit. The models and this calculational approach are reviewed in section .
